Higgs physics at the CLIC electron-positron linear collider

Abstract

The Compact Linear Collider (CLIC) is an option for a future [Formula: see text] collider operating at centre-of-mass energies up to [Formula: see text], providing sensitivity to a wide range of new physics phenomena and precision physics measurements at the energy frontier. This paper is the first comprehensive presentation of the Higgs physics reach of CLIC operating at three energy stages: [Formula: see text], 1.4 and [Formula: see text]. The initial stage of operation allows the study of Higgs boson production in Higgsstrahlung ([Formula: see text]) and [Formula: see text]-fusion ([Formula: see text]), resulting in precise measurements of the production cross sections, the Higgs total decay width [Formula: see text], and model-independent determinations of the Higgs couplings. Operation at [Formula: see text] provides high-statistics samples of Higgs bosons produced through [Formula: see text]-fusion, enabling tight constraints on the Higgs boson couplings. Studies of the rarer processes [Formula: see text] and [Formula: see text] allow measurements of the top Yukawa coupling and the Higgs boson self-coupling. This paper presents detailed studies of the precision achievable with Higgs measurements at CLIC and describes the interpretation of these measurements in a global fit.

Fig. 1

The luminosity spectrum for CLIC operating at $\sqrt{s}=3\text{TeV}$, where $\sqrt{s^{\prime }}$ is the effective centre-of-mass energy after beamstrahlung and initial state radiation [11]

Fig. 2

Longitudinal cross section of the top right quadrant of the CLIC_ILD (a) and CLIC_SiD (b) detector concepts

Fig. 3

Cross section as a function of centre-of-mass energy for the main Higgs production processes at an ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ collider for a Higgs mass of $m_{\mathrm{H}}=126\text{GeV}$. The values shown correspond to unpolarised beams and do not include the effect of beamstrahlung

Fig. 4

Leading-order Feynman diagrams of the highest cross section Higgs production processes at CLIC; Higgsstrahlung (a), $\mathrm{W}\mathrm{W}$-fusion (b) and $\mathrm{Z}\mathrm{Z}$-fusion (c)

Fig. 5

Feynman diagrams of the leading-order processes at CLIC involving (a) the top Yukawa coupling $g_{\mathrm{Htt}}$, and (b) the Higgs boson trilinear self-coupling $\mathit{\lambda }$

Fig. 6

Polar angle distributions for single Higgs events at $\sqrt{s}=350\text{GeV}$, 1.4 and $3\text{TeV}$, including the effects of the CLIC beamstrahlung spectrum and ISR. The distributions are normalised to unity

Fig. 7

Reconstructed invariant mass of $\mathrm{Z}\to {\mathrm{e}}^{+}{\mathrm{e}}^{-}$ candidates in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to \mathrm{Z}\mathrm{H}\to \mathrm{Z}\mathrm{W}{\mathrm{W}}^{\ast }$ events at $\sqrt{s}=350\text{GeV}$. Bremsstrahlung photons in cones of different opening angles around the electron direction are recovered as described in the text. All distributions are normalised to unity

Fig. 8

Reconstructed recoil mass distributions of ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to \mathrm{Z}\mathrm{H}$ events at $\sqrt{s}=350\text{GeV}$, where $\mathrm{Z}\mathrm{H}\to {\mathrm{\mu }}^{+}{\mathrm{\mu }}^{-}X$ (a) and $\mathrm{Z}\mathrm{H}\to {\mathrm{e}}^{+}{\mathrm{e}}^{-}X$ with bremsstrahlung recovery (b). All distributions are normalised to an integrated luminosity of $500{\text{fb}}^{-1}$

Fig. 9

Reconstructed di-jet invariant mass versus reconstructed recoil mass distributions for $\mathrm{Z}\mathrm{H}\to \mathrm{q}\overline{\mathrm{q}}X$ candidate events at $\sqrt{s}=350\text{GeV}$, showing $\mathrm{Z}\mathrm{H}$ signal events (a) and all background processes (b). In both cases the plots show all events passing the preselection

Fig. 10

Reconstructed recoil mass distributions of ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to \mathrm{Z}\mathrm{H}$ events at $\sqrt{s}=350\text{GeV}$, showing the $\mathrm{H}\to \text{invis.}$ signal, assuming $BR(\mathrm{H}\to \text{invis.})=100\%$, and SM backgrounds as stacked histograms. The distributions are normalised to an integrated luminosity of $500{\text{fb}}^{-1}$

Fig. 11

$\mathrm{b}\overline{\mathrm{b}}$ likelihood versus $\mathrm{c}\overline{\mathrm{c}}$ likelihood distributions for ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to \mathrm{Z}\mathrm{H}$ events at $\sqrt{s}=350\text{GeV}$, for (a) all events and for the different event classes: (b) H$\to$b$\overline{\mathrm{b}}$, (c) H$\to$c$\overline{\mathrm{c}}$, (d) H$\to$gg, background from (e) other Higgs decays and (f) non-Higgs SM background. All distributions are normalised to an integrated luminosity of $500{\text{fb}}^{-1}$

Fig. 12

Reconstructed Higgs candidate transverse momentum distributions for selected $\mathrm{H}\mathit{\nu }\overline{\mathit{\nu }}$ events at $\sqrt{s}=350\text{GeV}$, showing the contributions from Higgsstrahlung, $\mathrm{W}\mathrm{W}$-fusion and non-Higgs background. The distributions are normalised to an integrated luminosity of $500{\text{fb}}^{-1}$

Fig. 13

BDT classifier distributions for $\mathrm{H}\to {\mathrm{\tau }}^{+}{\mathrm{\tau }}^{-}$ events at $\sqrt{s}=350\text{GeV}$, showing the signal and main backgrounds as stacked histograms. The distributions are normalised to an integrated luminosity of $500{\text{fb}}^{-1}$

Fig. 14

Event display of a $\mathrm{H}\to {\mathrm{\tau }}^{+}{\mathrm{\tau }}^{-}$ event at $\sqrt{s}=1.4\text{TeV}$ in the CLIC_ILD detector. A 1-prong tau decay is visible in the central part of the detector (blue). The other tau lepton decays to three charged particles and is reconstructed in the forward direction (red). A few soft particles from beam-induced backgrounds are also visible (grey)

Fig. 15

Reconstructed Higgs invariant mass distributions for preselected $\mathrm{H}\to \mathrm{W}{\mathrm{W}}^{\ast }\to \mathrm{q}\overline{\mathrm{q}}\mathrm{q}\overline{\mathrm{q}}$ events at $\sqrt{s}=1.4\text{TeV}$, showing the signal and main backgrounds as stacked histograms. The distributions are normalised to an integrated luminosity of $1.5{\text{ab}}^{-1}$

Fig. 16

Reconstructed Higgs invariant mass distributions of $\mathrm{H}\to \mathrm{Z}{\mathrm{Z}}^{\ast }\to \mathrm{q}\overline{\mathrm{q}}{\mathrm{l}}^{+}{\mathrm{l}}^{-}$ events at $\sqrt{s}=1.4\text{TeV}$, showing the signal and main backgrounds as stacked histograms a after preselection, and b after the full event selection including a cut on the BDT classifier. The distributions are normalised to an integrated luminosity of $1.5{\text{ab}}^{-1}$

Fig. 17

Reconstructed di-photon invariant mass distribution of preselected signal $\mathrm{H}\to \mathrm{\gamma }\mathrm{\gamma }$ events at $\sqrt{s}=1.4\text{TeV}$. The distribution is normalised to an integrated luminosity of $1.5{\text{ab}}^{-1}$. The statistical uncertainties correspond to the size of the simulated event sample. The line shows the fit described in the text

Fig. 18

Event display of a $\mathrm{H}\to \mathrm{Z}\mathrm{\gamma }\to \mathrm{q}\overline{\mathrm{q}}\mathrm{\gamma }$ event at $\sqrt{s}=1.4\text{TeV}$ in the CLIC_SiD detector. Both jets are visible. The photon creates a cluster in the central part of the electromagnetic calorimeter (blue)

Fig. 19

Reconstructed di-muon invariant mass distribution of selected $\mathrm{H}\to {\mathrm{\mu }}^{+}{\mathrm{\mu }}^{-}$ events at $\sqrt{s}=3\text{TeV}$. The simulated data are shown as dots while the solid line represents the fit function described in the text. The dotted line shows the background contribution of the fit function. The distribution is normalised to an integrated luminosity of $2{\text{ab}}^{-1}$, assuming $-80\%$ electron polarisation

Fig. 20

Generated electron pseudorapidity ($\mathit{\eta }=-lntan\frac{\mathit{\theta }}{2}$) distributions for ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to \mathrm{H}{\mathrm{e}}^{+}{\mathrm{e}}^{-}$ events at $\sqrt{s}=1.4$ and $3\text{TeV}$. The distributions are normalised to 1.5 and $2{\text{ab}}^{-1}$ respectively. The vertical arrows show the detector acceptance

Fig. 21

Likelihood distributions for $\mathrm{H}\to \mathrm{b}\overline{\mathrm{b}}$ events in the ZZ-fusion analysis at $\sqrt{s}=1.4\text{TeV}$, shown for the signal and main background. The distributions are normalised to an integrated luminosity of $1.5{\text{ab}}^{-1}$

Fig. 22

Event display of a $\mathrm{t}\overline{\mathrm{t}}\mathrm{H}\to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}}\mathrm{q}\overline{\mathrm{q}}{\mathrm{\tau }}^{-}{\overline{\mathit{\nu }}}_{\mathrm{\tau }}$ event at $\sqrt{s}=1.4\text{TeV}$ in the CLIC_SiD detector. The tau lepton decays hadronically

Fig. 23

BDT classifier distributions for fully-hadronic $\mathrm{t}\overline{\mathrm{t}}\mathrm{H}$ events at $\sqrt{s}=1.4\text{TeV}$, shown for the $\mathrm{t}\overline{\mathrm{t}}\mathrm{H}$ signal and main backgrounds. The distributions are normalised to an integrated luminosity of $1.5{\text{ab}}^{-1}$. The vertical arrow shows the value of the cut, chosen to give the highest significance

Fig. 24

Feynman diagrams of leading-order processes that produce two Higgs bosons and missing energy at CLIC at $\sqrt{s}=1.4\text{TeV}$ and $3\text{TeV}$. The diagram (a) is sensitive to the trilinear Higgs self-coupling $\mathit{\lambda }$. The diagram (b) is sensitive to the quartic coupling $g_{\mathrm{H}\mathrm{H}\mathrm{W}\mathrm{W}}$. All four diagrams are included in the generated ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to \mathrm{H}\mathrm{H}{\mathit{\nu }}_{\mathrm{e}}{\overline{\mathit{\nu }}}_{\mathrm{e}}$ signal samples

Fig. 25

Cross section for the ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to \mathrm{H}\mathrm{H}{\mathit{\nu }}_{\mathrm{e}}{\overline{\mathit{\nu }}}_{\mathrm{e}}$ process as a function of the ratio $\mathit{\lambda }/{\mathit{\lambda }}^{\text{SM}}$ at $\sqrt{s}=1.4$ and $3\text{TeV}$

Fig. 26

Reconstructed di-jet invariant mass distribution of selected $\mathrm{H}\to \mathrm{b}\overline{\mathrm{b}}$ events at $\sqrt{s}=1.4\text{TeV}$, showing the signal and backgrounds as stacked histograms. The distributions are normalised to an integrated luminosity of $1.5{\text{ab}}^{-1}$

Fig. 27

Illustration of the precision of the Higgs couplings of the three-stage CLIC programme determined in a model-independent fit without systematic or theoretical uncertainties. The dotted lines show the relative precisions of 1 and 5%

Fig. 28

Illustration of the precision of the Higgs couplings of the three-stage CLIC programme determined in a model-dependent fit without systematic or theoretical uncertainties. The dotted lines show the relative precisions of 0.5 and 2.5%

Fig. 29

Illustration of the precision of the model-independent Higgs couplings and of the self-coupling as a function of particle mass. The line shows the SM prediction that the Higgs coupling of each particle is proportional to its mass